In his "Proofs and Refutations," Lakatos identifies the "Primitive Conjecture" as the first stage in the pattern of mathematical discovery. In this article, I am interested in ways of reaching the "Primitive Conjecture" stage in an undergraduate classroom. I adapted Realistic Mathematics Education methods in an abstract algebra class for the guided reinvention of quotient group concepts. From classroom instructional design experiments, students used mathematical observations to reach and prove "primitive conjectures." I conclude that mathematical observations form an important aid in making and proving conjectures and play the same role as observations in the scientific method.